Composites: Part A 104 (2018) 60–67

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Composites: Part A

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Kinetics and temperature evolution during the bulk polymerization ofmethyl methacrylate for vacuum-assisted resin transfer molding

https://doi.org/10.1016/j.compositesa.2017.10.0221359-835X/� 2017 Elsevier Ltd. All rights reserved.

⇑ Corresponding author at: Mechanical Engineering Department, Colorado Schoolof Mines, Golden, CO 80401, USA.

E-mail address: ysuzuki@mines.edu (Y. Suzuki).

Yasuhito Suzuki a,b,⇑, Dylan Cousins b, Jerred Wassgren b, Branden B. Kappes a, John Dorgan b,Aaron P. Stebner a

aMechanical Engineering Department, Colorado School of Mines, Golden, CO 80401, USAbChemical and Biological Engineering Department, Colorado School of Mines, Golden, CO 80401, USA

a r t i c l e i n f o

Article history:Received 16 August 2017Received in revised form 19 October 2017Accepted 21 October 2017Available online 23 October 2017

Keywords:Thermoplastic resinCure behaviorVacuum infusion

a b s t r a c t

Curing reactions of methyl methacrylate (MMA) comprise an induction time of gradual temperaturechange over tens of minutes, followed by a sudden temperature rise within tens of seconds because ofauto-acceleration known as the Trommsdorff effect. These curing effects were investigated as initial ini-tiator and polymer concentrations were varied. A mathematical model combining the reaction kineticswith heat transfer was developed and verified in its ability to simulate the processing kinetics and tem-perature evolutions throughout thick MMA-based parts. It was further demonstrated that the processingconditions at specific points within a part during manufacture could be actively controlled via theTrommsdorff effect by locally varying the initial concentration of poly(methyl methacrylate) (PMMA)solution. Together, these advancements provide an enhanced ability to design and optimize the manufac-ture of thick, large-scale PMMA materials by taking advantage of auto-acceleration instead of avoiding it.

� 2017 Elsevier Ltd. All rights reserved.

1. Introduction

The use of thermoplastic resin systems instead of thermosetscan improve the recyclability of composites, shorten the produc-tion cycle time, and reduce manufacturing costs. Although the con-cept has long been proposed, it is still challenging to fabricatethick, large-scale thermoplastic-based fiber-reinforced composites(FRCs) [1]. Vacuum-assisted resin transfer molding (VARTM) ismost commonly used to fabricate large FRCs like wind turbineblades [2] and ships [3]. With this method, fibers are placed on amold and shielded with a vacuum bag and vacuum tape. A low-viscosity thermoset resin and hardener are infused with the aidof a vacuum. The resin is then cured at a high temperature [4,5].There are two approaches to using thermoplastic resin: melt infu-sion and reactive processing. Because the viscosities of polymermelts are too high at a reasonable temperature in a vacuum, reac-tive processing is a practical approach. Promising systems includering-opening polymerization of nylon [6–10] and free-radical poly-merization of acrylics [1]. In this study, we focus on the poly(methyl methacrylate) (PMMA)-based system.

Acrylics are widely used in many applications, including win-dow glass substitutes and FRCs. An acrylic polymer such as PMMAis cost-efficient and provides comparable tensile modulus toepoxy. PMMA can be synthesized via free-radical bulk polymeriza-tion of MMA [11,12]. The PMMA reaction can be initiated by ben-zoyl peroxide in the presence of an amine at room temperature. Inother words, a separate heating device is not required for the initi-ation of the reaction. A key issue to be addressed is the thermalmanagement during the curing reaction. The heat of polymeriza-tion of MMA to PMMA is 57.8 kJ/mol [13], which is around threetimes greater than a typical epoxy resin. In addition, it is knownthat the bulk free-radical polymerization reaction will auto-accelerate due to the gel (Trommsdorff) effect [14]. The phe-nomenon originates from the sudden drop of the termination ratedue to the increased viscosity of the resin [15,16]. After an induc-tion period, the temperature increases dramatically. To make high-quality parts, thermal runaway has to be avoided; the temperatureshould not exceed the boiling point of the monomer, which isapproximately 100 �C at ambient pressure [13].

Thus, to design the manufacturing of PMMA parts, it is desirableto predict the induction time, the maximum temperature, and thetotal reaction time. Toward this goal, we proceed to study the cur-ing kinetics of free-radical polymerization of MMA with variousinitial initiator and polymer concentrations. We then develop a

Y. Suzuki et al. / Composites: Part A 104 (2018) 60–67 61

model that can be used to design the manufacture of parts. Bulkpolymerization curing kinetics of PMMA have been extensivelyinvestigated in the past [15–20]. Although most models stillrequire some assumptions or artificial functions to capture thegel effect, they can be reasonably calibrated to predict the curingkinetics [21]. In this study, we advance these models by combininga curing model [19] and a one-dimensional heat transfer equationto simultaneously predict the temperature evolution. This com-bined model is desired to design the manufacturing process forlarge, thick parts. For thermoset resins, a simple model or even justdifferential scanning calorimetry (DSC) data can be used to designan infusion process, but the auto-acceleration nature of bulk free-radical polymerization is very sensitive to the initial conditions andboundary conditions, namely, the temperature evolution duringthe cure. Lastly, we draw upon the Trommsdorff effect to proposeand demonstrate a method for further active temperature controlthroughout the part by locally grading the viscosity of the resinthrough variations in the initial PMMA concentrations to achievedifferent curing kinetics and thermodynamics at different materialpoints within the parts.

Fig. 1. Temperature profile during the bulk free-radical polymerization of methylmethacrylate initiated by benzoyl peroxide in the presence of an amine at roomtemperature.

2. Methods

(a) Materials

Methyl methacrylate (MMA), N,N-dimethyl-p-toluidine (DMT)and benzoyl peroxide (BPO: Luperox� AFR40) were purchasedfrom Sigma-Aldrich. The MMA inhibitor was removed using pre-packed column inhibitor removers (Sigma-Aldrich). Poly(methylmethacrylate) (PMMA) (Mw = 99 kg/mol, PDI = 1.2) was obtainedfrom commercial sources and used as received. For all but oneexperiment, the resin was formulated with 800 g of MMA, 200 gof PMMA and 5.3 g of N,N-dimethyl-p-toluidine. For the experi-ment studying the effect of pre-dissolved PMMA (Fig. 6), the molarratio of MMA, N,N-dimethyl-p-toluidine, and BPO (269:1:1) werekept constant while the amount of pre-dissolved PMMA was var-ied. In this study, ‘‘cure” refers to the in situ polymerization ofresin.

(b) Temperature measurement using thermocouples

Temperature as a function of time was measured using ther-mocouples and a data logger from National Instruments. J-Typethermocouples were connected to a 4-Ch thermocouple input(NI 9211), and data were collected with a USB data logger(NI cDAQ-9171). For the small-scale experiments, resin andinitiator with a total weight of 6.0 g were well mixed in a20 ml scintillation vial. To avoid evaporation, a hole was drilledin a lid with an aluminum backing, and a thermocouple wasinserted through the hole. In addition, the gap between the lidand the thermocouple was sealed using a vacuum bag sealanttape. The scintillation vial with the sample was placed in aconstant temperature stirred oil bath.

(c) Temperature measurement during the VARTM with an IRcamera

An IR camera (FLIR A325sc) was used to record the temperatureevolution during the cure of a panel fabricated via the VARTM pro-cess. A VARTM setup was developed to infuse a 30 cm by 30 cmpanel. Glass fibers, peel ply, and infusion flow media (purchasedfrom Fibre Glast) were placed on a glass mold and sealed with vac-uum tape and a vacuum bag. The MMA-based resin was theninfused. The IR camera was positioned at a height of about 70 cmon a tripod set at a 90� angle capture the heat signature of theinfusion and subsequent cure.

(d) Simulation technique

The coupled equations of curing kinetics and heat transfer thatwe develop in Section 3 were numerically solved using WolframMathematica (version 11.0). As shown in the supporting informa-tion (Fig. S1), typical radical concentration was on the order of10�16 lower than the initial monomer concentration; thus, thecomputation requires high working precision. Hence, 24 digitsworking precision was used. An accuracy goal, which specifiesthe effective digits of accuracy in the final result, was set to 18 dig-its for this computation, which showed convergence and stabilityrelative to a choice of 10 digits (Fig. S1).

For the simulations that accounted for spatial geometry (Figs. 7and 8), the model parameters were simplified to speed up the com-putations (a single simulation of the full kinetic model had notcompleted in 2 weeks on a 32-core, 256 GB RAM workstation).The kinetic parameters are treated as constants, using their valuesat 323 K. In addition, thermal conductivity (0.12 W/(m K)), densityof the matrix (2.0 kg/m3), and the heat capacity (1.4 kJ/(kg K)) areheld constant using the averaged values of PMMA and glass fibers.

3. Results and discussion

3.1. Temperature profile during the polymerization reaction

Fig. 1 shows an example of the temperature profile during thecuring reaction of the MMA-based resin. The resin contained 20wt% pre-dissolved PMMA and exhibited a comparable viscosityto epoxy resin. The reaction was initiated by benzoyl peroxide inthe presence of an amine (N,N-dimethyl-p-toluidine). The redoxreaction of benzoyl peroxide by the amine generates radicals, evenat room temperature [29,30]. The temperature gradually increasedfor the first 35 min. During this time, the termination rate of thegrowing macroradicals was governed by the ability of the radicalchain ends to diffuse and orient to each other. This phenomenonis known as segmental diffusion. Translational diffusion (move-ment of the entire macroradical through the solution) is not hin-dered at the beginning of the reaction because the solution isdilute. Once the solution becomes concentrated enough, termina-tion is further limited by translational diffusion. During this periodthe temperature of the solution begins to display a noticeableincrease, though it is not extremely rapid. Translational diffusionwas observed from 35 to 40 min in Fig. 1. After this initial induc-tion time through the first two phases, the temperature of the resin

Fig. 2. (Left) Experimental setup to measure the temperature evolution during the curing reaction of resin. (Right) Temperature profiles as a function of time for differentconcentrations of the initiator. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 3. Comparison of the experimental (dashed lines) and simulated (solid lines)temperature evolutions during the free-radical polymerization reactions. (Forinterpretation of the references to color in this figure legend, the reader is referredto the web version of this article.)

Fig. 5. Temperature profiles during the cure of MMA with different amounts of pre-dissolved PMMA. Here, the molar ratio of reactive species (i.e., MMA, amine, andBPO) is kept constant. (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this article.)

62 Y. Suzuki et al. / Composites: Part A 104 (2018) 60–67

begins to increase dramatically. Within 3 min, the temperaturechanged from 35 �C to 70 �C. This auto-acceleration of the reactionkinetics is known as the Trommsdorff effect. This effect arises due

Fig. 4. Conversion as a function of time with different initiator concentrationspredicted by the model. The onset of the Trommsdorff effect correlates with theconversion. (For interpretation of the references to color in this figure legend, thereader is referred to the web version of this article.)

to both the entire macroradical and its chain ends being trapped inthe viscous and entangled solution. At this point, the rate of termi-nation drops dramatically, but the monomer units are still able todiffuse through the viscous liquid. Therefore, the overall reactionrate increases dramatically.

The increased viscosity affects kinetic parameters; in particular,the rapid drop in the termination rate impacts the total kinetics.The individual radicals are trapped due to the high viscosity ofthe matrix, and the chance to terminate with another radicaldecreases. As a result, more and more radicals continue reacting,and more heat is generated per a unit time. The generated heatincreases the temperature and further speeds up the reaction;hence, the system has an auto-acceleration nature. For the applica-tion purpose to FRCs, the induction time corresponds to the pot lifeof the resin. The total reaction time determines the cycle time. Inaddition, controlling the maximum temperature below the boilingpoint of the monomer is critically important to avoid the bubbleformation.

In this study, the temperature evolution was tracked using ther-mocouples, as shown in Fig. 2 (left). A total of 6 g of the resin andthe initiator were mixed in the scintillation vial. The scintillationvial was placed in a constant temperature oil bath. A hole was

Fig. 6. A demonstration of reaction control by locally varying viscosities. (Top) A 40 wt% PMMA in MMA solution was pasted at four different spots in between glass fibers.(Bottom) Because of the local viscosification, the Trommsdorff effect starts at the four spots. The thermal image was captured by IR camera.

Fig. 7. (a) Scheme of the model with a spatial geometry. 50 vol% resin and 50 vol% glass fibers are placed in between constant-temperature walls. (b) An example of thecomputational result with a thickness of 30 cm.

Y. Suzuki et al. / Composites: Part A 104 (2018) 60–67 63

drilled in the lid, and a thermocouple was inserted through thehole. To minimize the evaporation, the gap between the thermo-couple and the lid was sealed with a yellow vacuum tape. Fig. 2(right) plots the temperature profile during the cure for differentamounts of the initiator. The temperature profiles strongly dependon the initiator concentrations. While the induction time was �60min with 0.5 wt% initiator concentration, it shortened to �15 minwith 5.0 wt% initiator concentration. Furthermore, the maximumtemperature tends to become higher with a higher initiator con-centration. The temperature profile also depends on the heat dissi-pation by the heat transfer; thus, the volume-to-surface ratio of thecontainer, the materials of the container, and the surroundingenvironment affect the temperature profile.

3.2. One-dimensional heat transfer model

As mentioned in the introduction, predicting the pot life, theproduction cycle time, and the maximum temperature during thecure enables better applications of the resin. The temperature pro-file is a result of the competition between the heat generated bythe reaction and the heat dissipated by the heat transfer. Assumingthat the heat generated is proportional to the monomer consumedby chemical reaction, and heat transfer can be approximated by asimple one-dimensional term, temperature (T) change as a func-

tion of time (t) by chemical reaction and a simple one-dimensional heat transfer can be written as follows:

dTdt

¼ DHPMMA

m � cP � v � �dMMMA

dt

� �� h � Am � cP ðTðtÞ � TcoldÞ ð1Þ

In Eq. (1), DHPMMA is the heat of polymerization of PMMA, m is thetotal mass, v is the total volume, cP is the heat capacity, MMMA is themass of the monomer (MMA), h is the heat transfer coefficient andTcold is the temperature of the surroundings. In Eq. (1), the first termis the heat generation by the polymerization reaction and the sec-ond term denotes the heat dissipation by the heat transfer to thesurroundings.

To determine the first term in Eq. (1), a model of the reactionkinetics is needed. After the research by Trommsdorff, a numberof studies have attempted to model the kinetics of bulk free-radical polymerization. The difficulty in developing a kinetic modelis that all the kinetic parameters are functions of both conversionand temperature in a complex manner. As conversion increases,the solution changes from dilute regime to semi-dilute regimeand, eventually, concentrated regime [22–24]. Depending on theconcentration and molecular weight of the polymer in the resin,the polymer starts to be entangled at some point of the reaction.The property of the resin affects translational diffusion, rotationaldiffusion, and segmental dynamics of polymer chains. To take all

Fig. 8. Temperature evolution as a function of time in between two plates with different thicknesses. Given the formulation of the resin and thermal conductivity of theplates, there is a maximum thickness to cure without reaching the boiling point of the resin.

Scheme 1. Kinetic scheme for free-radical polymerization initiated by benzoylperoxide in the presence of an amine. The superscript * indicates radicals.

64 Y. Suzuki et al. / Composites: Part A 104 (2018) 60–67

the factors into account, models require some assumptions orempirical statements. Nevertheless, some of the models are suc-cessful in predicting the curing kinetics.

Achilias et al. demonstrated a mathematical model for anacrylic resin initiated with BPO and an amine for application inthe field of dentistry [18] based on a previously developed mathe-matical framework [17]. Recently, Zoller et al. reported a mathe-matical model of MMA polymerization initiated by BPO in thepresence of N,N-dimethyl-p-toluidine [19]. In the current study,we followed these two approaches. The model used herein is basedon the free-volume ideas. It assumes that the free-volume changedue to the reaction governs the diffusion controlled initiation andpropagation. The effect of free-volume on the initiation was mod-eled by introducing the efficiency parameter of the initiation reac-tion (Table S3, Eq. (S6)). The efficiency parameter is an empiricalequation and was adjusted to capture the experimental result(Table S2). For the propagation, the free-volume change wasrelated to the diffusion coefficient of the monomer as describedin Eq. (2).

Dm½t� ¼ Dm;0 � exp � cmVf ½t�

� �ð2Þ

Here, Vf ½t�, Dm;0, Dm½t� and cm denote the free volume, the initial dif-fusion coefficient, the diffusion coefficient, and the overlapping fac-tor, respectively. The diffusion coefficient of monomer affects theeffective kinetic parameters, as shown in Eq. (3).

1keff ½t� ¼

1k0

þ 14pNArpDm½t� ð3Þ

Here, keff ½t�, k0, NA, and rp express the effective kinetic parameter,the initial kinetic parameter, Avogadro’s constant, and the reactionradius, respectively. In Eq. (3), the first term (k0) is kinetically con-trolled, while the second term (4pNArpDm½t�) is controlled by the dif-fusion [21]. At a higher conversion, the second term dominates theeffective kinetic parameter. The same equation structure was usedfor the transfer coefficients as well.

The kinetic scheme for the polymerization initiated by BPO inthe presence of an amine is presented in Scheme 1. In addition tothe main reactions of decomposition, initiation, propagation, andtermination, side reactions by chain transfer reactions are also con-sidered. Based on Scheme 1, balance equations can be derived, as

Y. Suzuki et al. / Composites: Part A 104 (2018) 60–67 65

illustrated in Scheme 2. These kinetic parameters are a function oftemperature; thus, these parameters are coupled to Eq. (1). All theparameters used are summarized in the Supporting Information[25–28]. One empirical statement in the model is the terminationrate constant (kt). The termination constant is described by fourdifferent regions depending on the conversion [20,21]. These equa-tions were entered in Wolfram Mathematica and numericallycalculated.

The temperature evolutions as a function of time for varyinginitiator concentrations were simulated using the mathematicalmodel. For the heat of polymerization, a value estimated from aDSC study (28.5 kJ/mol) was employed. The value is lower than avalue reported from a polymerization in a solvent. This is partiallydue to the evaporation of the monomer from the surface. As thereaction proceeds, some parameters (i.e., density, heat capacity,and thermal conductivity) change because the amount of PMMAin the matrix increases. However, these changes are small, andthey are treated as constants using average values in the model.One parameter that needs to be obtained from the experiment isthe heat transfer coefficient. For practical applications, the heattransfer coefficient depends a lot on the material, the geometry,and the surrounding environment of the mold. It is therefore nec-essary to obtain or estimate a mold-specific heat transfer coeffi-cient. Here, we used one of the experimental data and adjustedthe heat transfer coefficient so that the maximum temperaturesof the experiment and of the model agree. The obtained heat trans-fer coefficient was fixed for the rest of the simulation in this study.The simulated results are plotted in Fig. 3 (solid line). As a compar-ison, the corresponding experimental data are also presented inFig. 3 (dashed line). The model reasonably captures the inductiontime and the maximum temperature when the initiator concentra-tions are changed.

The model also provides the profile of all the parameters as afunction of time. Some of them are difficult to access experimen-tally. Fig. 4 depicts the conversion as a function of time. Because20 wt% of pre-dissolved PMMA was added, the conversion (x½t�)was defined as follows:

x½t� ¼M½0�

ð1�P0Þ �M½t�M½0�

ð1�P0Þð4Þ

Scheme 2. List of balance equations and heat transfer e

Here, M½0�, M½t�, and P0 denote the initial monomer concentration,the monomer concentration at time t, and the relative amount ofpre-dissolved PMMA, respectively. Because of the definition, theconversion starts from 0.2 in Fig. 4. The final conversion decreasesas the initiator concentration decreases. The model implies thatthe Trommsdorff effect starts at a conversion of 0.4.

3.3. The effect of pre-dissolved PMMA and an application

The previous result described in Fig. 5 allows for another way ofcontrolling the reaction time. Because the onset of the Tromms-dorff effect correlates with the viscosity of the matrix, the amountof pre-dissolved PMMA can be manipulated to control the induc-tion time and the cycle time. Fig. 6 displays the effect of pre-dissolved PMMA. In this experiment, the molar ratio of reactivespecies (i.e., MMA, N,N-dimethyl-p-toluidine, and BPO) was keptconstant. The induction time shortens from 45 min (0 wt% PMMA)to 8 min (30 wt% PMMA). It is noted that if it were a solvent insteadof pre-dissolved PMMA, it would just dilute the concentrations ofthe reactive species and slow the total reaction time.

The mathematical model can simulate these phenomena. Thedifferent amounts of pre-dissolved PMMA were inserted in Eq.(4). The computed result is provided in Fig. S2. While the modelqualitatively predicts the shortening of the induction time by add-ing the pre-dissolved PMMA, the obtained induction times areslightly different from the experiments. In addition, the modelshows a decrease of the maximum temperature with addition ofpre-dissolved PMMA. This trend is not observed in the experimen-tal result. One possible explanation is that the model does not takeinto account the effect of molecular weight distribution. It isknown that the molecular weight distribution of bulk free-radicalpolymerization is very broad [19]; thus, the matrix, in reality,becomes very inhomogeneous. The inhomogeneous environmentmay affect the reaction kinetics (i.e., the induction time and themaximum temperature).

In a practical application for VARTM processing, the desired vis-cosity range of the initial resin is predetermined by the vacuumsetups and the mold; thus, the control of the induction time bythe amount of pre-dissolved PMMA in the resin is limited. On theother hand, the phenomenon can be used to locally control the

quations. These differential equations are coupled.

66 Y. Suzuki et al. / Composites: Part A 104 (2018) 60–67

reaction kinetics by a local viscosification. The concept is demon-strated in Fig. 6. A highly concentrated solution of PMMA inMMA (40 wt%) was placed on the four spots of glass fiber sheetas indicated by black circles. One more glass fiber sheet was placedon top to avoid the direct contact of the high-concentration PMMAsolution to the peel ply. Then, a VARTM infusion was conducted asusual using a resin containing 20 wt% pre-dissolved PMMA. Thetemperature profile during the cure was captured using an IR cam-era. The IR camera image shows that the onset of the Trommsdorffeffect started at the same position where a high-concentrationPMMA solution was pasted. The infused resin was locally viscosi-fied at the spots, so the kinetic parameters change at these posi-tions, accelerating the onset of the Trommsdorff effect. Toquantify this effect, temperature profiles at two different spotsare extracted and plotted in Fig. S3. Instead of a high-concentration PMMA solution, a thin film of PMMA can be placedfor the same effect. Since the phenomenon originates from thelocal viscosification, another polymer that is miscible with MMAcan also be used. One important parameter is the dissolution kinet-ics to the resin. The dissolution must be completed in a reasonabletime range to control the phenomenon. For a practical application,a further engineering is needed, including determining how toplace the reaction spots. The method opens a possibility to curethe resin without any extra heating device. Because the reactionis highly exothermic, the active control of the onset of the Tromms-dorff effect enables regulation of the temperature within a desiredrange.

3.4. Two-dimensional model

The developed model can be expanded taking into account spa-tial geometry. Here, the model shown in Fig. 7(a) is considered. Theresin and the glass fibers are placed in between two walls withfixed temperatures. The temperature profile can be written asfollows:

dTdt

¼ DHPMMA

q � cP � �dMMMA

dt

� �� jq � cP

@2T@x2

!ð5Þ

The differences from Eq. (1) are the j and x parameters, whichdenote thermal conductivity and the distance between the walls,respectively. Eq. (5) can be coupled with the balance equations inScheme 2. A computational challenge is that the differential equa-tions are very stiff. Combined with the huge dynamic range of theconcentration of reactive species, the computation becomesexpensive. For a qualitative understanding with a reasonable com-putation time, we fixed kinetic parameters at 323 K. A computa-tional result with a 30 cm thick wall is shown in Fig. 7(b).Because of the simplified kinetics, the induction time and the max-imum temperature are not precise; however, the computation cap-tures the qualitative temperature profiles as functions of time andposition.

Using the extended model, the dependence on wall thicknesswas studied. Fig. 8 shows the temperature profile as a function oftime and position at different thicknesses. The temperature isscaled from 27 �C to 100 �C. The important outcome is that themaximum temperature at the center position strongly dependson the thickness. The thicker the panel, the more difficult it is todissipate heat within a given time frame. In this example, whilethe temperature only reached 40 �C at a thickness of 20 cm, itexceeded the boiling point of the monomer at a thickness of 40cm. These results imply that for a given chemical formulation ofthe resin and the heat transfer from the mold, there exists a max-imum wall thickness that can be used to avoid the boiling of themonomer.

4. Conclusion

Reaction kinetics and temperature evolution during the poly-merization of MMA were investigated. Because of the Trommsdorffeffect, the temperature increases rapidly after an induction time.The important parameters for VARTM (i.e., pot life, cycle time,and the maximum temperature) depend on the chemical formula-tion and the heat transfer. A mathematical model based on thereaction kinetics and heat transfer equation was developed to sim-ulate these behaviors. Furthermore, it was demonstrated that theaddition of pre-dissolved PMMA increases the viscosity of the resinand changes the kinetic parameters locally. We specifically showedthat the induction time shortens from 45 min for 0 wt% PMMA to 8min for 30 wt% PMMA. This phenomenon can be used intentionallyto control the position where the Trommsdorff effect starts. Theconcept was demonstrated by placing 40 wt% PMMA solution atfour spots during the VARTM cure. Lastly, it was demonstrated thatthe mathematical model can be used to calculate the maximumthickness allowed to cure the resin without reaching the boilingpoint of the monomer with fixed chemical formulation and ther-mal conductivity. These results will be particularly advantageousfor designing the manufacture of thick fiber-reinforced materialswith PMMA matrix, especially as geometries become complex,such as geometries of variable thicknesses.

Acknowledgments

The authors gratefully acknowledge financial support from theState of Colorado Office of Economic Development and Interna-tional Trade Advanced Industries Program (senior program man-ager Katie Woslager) and Colorado Higher Education CompetitiveResearch Authority (CHECRA) through their commitment to theInstitute for Advanced Composites Manufacturing and Innovation(IACMI) Wind Energy program.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at https://doi.org/10.1016/j.compositesa.2017.10.022.

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